论文标题
基于非交通图的梯度近似和多变量的无衍生物优化
Gradient Approximation and Multi-Variable Derivative-Free Optimization based on Non-Commutative Maps
论文作者
论文摘要
在这项工作中，开发了针对无约束优化问题的多变量无衍生化优化算法。引入了一种基于非交通图的多变量目标函数梯度的新方法。该过程基于构造探索顺序，以指定评估目标函数的位置以及与目标函数组成的所谓梯度生成函数的定义，从而模仿了梯度下降算法。研究了所提出的算法类别的各种理论特性，并提供了数值示例。
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps is introduced. The procedure is based on the construction of an exploration sequence to specify where the objective function is evaluated and the definition of so-called gradient generating functions which are composed with the objective function such that the procedure mimics a gradient descent algorithm. Various theoretical properties of the proposed class of algorithms are investigated and numerical examples are presented.
